Before explaining the meaning of the “\(\mathbf {a}\) -value” and “\(\mathbf {a}(2)\) -finite”, let us briefly summarize for context
some known results about Kazhdan–Lusztig cells. For Weyl groups of types \(A\) , \(B\) , \(D\)  and affine \(A\) , the cells
may be obtained via various combinatorial models involving Young tableaux, the Robinson–Schensted correspondence,
and their suitable generalizations; see [1]}, [2]} for type \(A\) ,
[3]}, [4]}, [5]} for types \(B\)  and \(D\) , and [6]}, [7]} for type
affine \(A\) . Cells of some other specific Coxeter systems (especially those with small ranks or complete Coxeter
diagrams) have also been computed, often on a case-by-case basis via carefully designed algorithms. For example,
the paper [8]} treats cells in the Coxeter group \(F_4\) , [9]} treats \(\tilde{C}_4\) ,
[10]} treats \(H_3\)  and \(H_4\) , [11]} and [12]} treat \(E_8\) ; the paper
[13]} studies
affine Weyl groups of rank 2, and the papers [14]}, [15]} deal with Coxeter systems with complete Coxeter
diagrams. For a more comprehensive summary of the cell literature, see [16]}.
